%\documentclass[beamer]{standalone}
\documentclass{standalone}\usepackage{beamerarticle}\newenvironment{standaloneframe}{}{}
\usepackage{tikz}

\begin{document}
  \tikzset{
    small dot/.style={
      inner sep=0,
      fill,
      minimum size=4pt,
      circle
    }
  }
  \begin{standaloneframe}
%    \begin{overprint}
  \begin{tikzpicture}
    \def\radius{3}
    \def\dist{4}
    \def\ddist{3}
    \def\da{40}

    \def\spherarea{
    \node (stacja) at (0,0) [small dot,label={$S$}]{};
    \draw [fill=gray!20]
    (\da/2:\dist-\ddist/2) 
    arc (\da/2:-\da/2:\dist-\ddist/2)
    --(-\da/2:\dist+\ddist/2)
    arc (-\da/2:\da/2:\dist+\ddist/2)
    --cycle
    ;

    \draw[latex-latex](-\da/2:\dist)
    arc (-\da/2:\da/2:\dist)
    ;
    \node [right]at (0:\dist){$\rm d A$};
    }

    \only<1>{
    \spherarea

    \draw[latex-latex,thick]
    (stacja)--+(0:\dist)node [above,midway]{$\psi$};
    \draw[latex-latex,thick]
    (stacja)
    ++(-\da/2:\dist-\ddist/2)
    --
    +(-\da/2:\ddist)
    node [below,midway,sloped] {$\rm d \psi$};
    ;
  }
    \mode<article>{
    \begin{scope}[shift={(7,0)}]
    }
    \mode<beamer>{\pause}
    \spherarea

    \draw[latex-latex,thick]
    (stacja)--+(0:\dist-\ddist/2)node [above,midway]{$\psi_1$};
    \draw[latex-latex,thick]
    (stacja)
    --
    +(-\da/2:\dist+\ddist/2)
    node [below,midway,sloped] {$\psi_2$};
    ;
    \mode<article>{
    \end{scope}
  }
  \end{tikzpicture}
%  \end{overprint}
\end{standaloneframe}
\end{document}
